Saturation mechanism of a storage ring free electron laser: An analytic model

An analytical solution of the optical pulse evolution equation in a storage ring free electron laser under the assumption of long electron pulse with parabolic shape is obtained by exploiting recent results in the operational calculus associated to exponential operators. The intracavity laser power is coupled to the induced electron beam energy spread evolution equation. The model also includes other saturation mechanisms: the electron beam bunch lengthening, causing a reduction of the peak current, and the longitudinal synchronism between laser and electron pulses.